Spurious Q-values in C12-breakup

Volume 4, number 2

PHYSICS

SPURIOUS

LETTERS

Q-VALUES

IN

15 March 1963

C12-BREAKUP

N. K. SHERMAN ¢ Queen's University, Kingston, Ontario, Canada Received 12 F e b r u a r y 1963

An e x c i t e d s t a t e of Be 8 at 4 M e V r e p o r t e d 1) to p a r t i c i p a t e in the C12(7, c~)Be 8 * r e a c t i o n h a s not b e e n o b s e r v e d in c~ - c~ s c a t t e r i n g o r in L i 8 d e c a y ( r e f . 2-4)). E v i d e n c e i s g i v e n h e r e to s h o w t h a t t h i s p e a k in the d i s t r i b u t i o n of p r o n g - p a i r Q - v a l u e s i s s p u r i o u s , b e i n g due to r e s o n a n t a b s o r p t i o n of p h o t o n s into the 15.11 M e V s t a t e of C 12. T h e e n e r g i e s of o t h e r a b s o r p t i o n r e s o n a n c e s a r e o b t a i n e d f r o m s i m i l a r p e a k s v i a a l i n e a r r e l a t i o n b e t w e e n the s p u r i o u s Q - v a l u e s and the photon e n e r g i e s . T h e d i s t r i b u t i o n of p o s s i b l e Be 8 Q - v a l u e s f o r 679 t h r e e - p r o n g e d s t a r s p r o d u c e d in 100 # I l f o r d K2 e m u l s i o n s by 70 MeV b r e m s s t r a h l u n g i s shown in fig. 1. T h e s h a d e d p o r t i o n of the h i s t o g r a m c o n t a i n s a l l the Q - v a l u e s of s t a r s f o r which at l e a s t one fell between 2.4 MeV and 3.6 MeV. In "coincidence" with the 3.0 MeV peak are several satellites. When the bins are widened to 0.4 MeV and a smooth curve is fitted 5) to the shaded data, the satellite energies are as given in the first column of table I. A momentum-balance analysis shows that these peaks are not due to misidentification of the events. One calculated Q-value is valid for each star in which Be8 took part. The two spurious ones e i are given by 1

L Ec~ + El) - (Ec~Ei)~ COS~i, ®i = ~(

i = 1,2 ,

(I)

where Ec~ is the energy of the first a-particle emitted "n the breakup of C12, E~is the energy of one of the (~'s originating in the Be° decay, and ~i is the angle between the two tracks. Momentum conserva-

j

;

I

J

f

i

I

I

l

I

I

l

I

I

i

r

I

r

I

i

i

® (MeV)

Ey (MeV)

Ez (MeV)

3.6

14.1

4.3

15.0

5.3

16.3

15.6

(6.2)

(17.5)

17.8

6.9

18.5

7.7

19.5

19.3

(8.3) (9.8)

(20.3) (22.3)

21.0

22.2

10.5

23.3

22.8

23.3

21.0

tion r e q u i r e s that Eol=

2

1

(~)E K

-~E

E K=

E./

(E 5 + Q) ,

-

I

.

I t

I I

-

Lr"- IJ~ n Will

[] ° ~ . . . . . . . . .

n

IP~

-Ul, ~llt

2.4~O~<3.6Mev.

® =

~(E~ + 1

I

1

~) -

(E~)~

g

. . . .

o ,,, o . . . . .

~b . . . . 0 ( MeW

,g

. . . .

Fig. 1. Calculated Q-values.

z'o

1

c o s ( , - ~ ~) ,

(4)

B ,

(5)

w h e r e E B is the c o r r e s p o n d i n g k i n e t i c e n e r g y of r e c o i l of the b e r y l l i u m n u c l e u s . Therefore,

'°~

G . . . . .

(3)

w h e r e E., i s the photon e n e r g y and E 5 i s the m a s s d e f e c t 0 / 3 He 4 c o m p a r e d to C 12. F o r a p a r t i c u l a r E~/ r a n d o m l y - o r i e n t e d b r e a k u p of Be 8 with l i b e r a tion of m o s t p r o b a b l e e n e r g y Q will g e n e r a t e a s p u r i o u s p e a k of e n e r g y

1

llF ~ I

(2)

0 ,

w h e r e E o is the ( n e g l i g i b l e ) r e c o i l e n e r g y of the C 1 2 - n u c l e u s due to the photon m o m e n t u m , and

E=½Q+~E ILl

E(y,n)

w h e r e E i s the m o s t p r o b a b l e e n e r g y of the two c~p a r t i c l e s f r o m Be 8 and 0 is the m o s t p r o b a b l e a n g l e b e t w e e n t h e m in the l a b o r a t o r y s y s t e m . Energy conservation gives

¢ P r e s e n t address: Centre d'Etudes Nuel~aires de Saelay, France. ~ I

Table 1. Spurious Q-values and corresponding photon absorption resonances.

....

2"5

= }o + }Q + E~.

(6)

If the s t a t e of Be 8 c o r r e s p o n d i n g to Q h a s width r Q , the ~ - p e a k s will h a v e widths of at l e a s t ~ F Q e v e n if the a b s o r p t i o n r e s o n a n c e i s s h a r p . F o r 113

Volume 4, number 2

PHYSICS LETTERS

E = 15.11MeV, Q = 3.0MeV, andE 5 = 7.275MeV, e~. (6) g i v e s ® = 4.38 MeV. The 4 MeV peak 1) had a width s o m e w h a t l e s s than 0.3 MeV which a g r e e s with ~1 r Q s i n c e the 2.90 MeV s t a t e of Be 8 is about 1.2 MeV wide, and with the p r e s e n t e x p e r i m e n t , w h e r e all the widths w e r e of about 0.3 MeV. The width of the 15.11 MeV l e v e l (75 eV) is n e g l i g i b l e in c o m p a r i s o n . V a l u e s of E ~ c a l c u l a t e d f r o m the d a t a u s i n g (6) a r e shown in table 1. T h e y a r e c o m p a r e d with the e n e r g i e s E a at which r e s o n a n c e s w e r e found in the c r o s s s e c t i o n c u r v e , and with the E(~, n) found by M i l l e r et al. 6) u s i n g m o n o e n e r g e t i c photons. T h e o c c u r r e n c e of (~, 3a) r e s o n a n c e s at the s a m e e n e r gies as (~, n) r e s o n a n c e s i s u n e x p e c t e d ; n o n e t h e l e s s , a d e f i n i t e peak at 22.8 MeV in the c r o s s s e c t i o n c u r v e s u p p o r t s the o b s e r v a t i o n .

A NEW

SIZE

15 March 1963

T h a n k s a r e due to M r . F. S a p i e n z a and M r . L. Hawke for s c a n n i n g and m e a s u r e m e n t s , to P r o f . P. A. P u h a c h for helpful c r i t i c i s m and to P r o f . B. W. S a r g e n t for his i n t e r e s t in this work.

References 1) F.K. Goward and J.J.Wilkins, Proc. Roy. Soc. London A228 (1955) 376. 2) R.H.Spear, Australian J. Phys. 11 (1958) 502. 3) D.Bredin et al., Proe. Roy. Soc. London A251 (1959) 143. 4) J. Cerny, B.G. Harvey and R. H. Pehl, Nuclear Phys. 29 (1962) 120. 5) E. P. F e r r e i r a and P.J.Waloschek, Proc. Intern. Conf. Peaceful Uses of Atomic Energy, Vol. 2 (1955) 124. 6) J . M i l l e r et al., Physics Letters 2 (1962) 76.

EFFECT

P. C O T T I Institut fur kalorisehe Apparate und K~lteteehnik, Swiss Federal Institute of Technology, ZUrich, Switzerland Received 16 February 1963

It is well known that the e l e c t r i c a l r e s i s t i v i t y p of a s p e c i m e n i n c r e a s e s above that of the bulk m a t e r i a l Pb when its d i m e n s i o n s b e c o m e c o m p a r a b l e to o r s m a l l e r than the e l e c t r o n i c m e a n f r e e path l b of the bulk m a t e r i a l . S i m i l a r l y eddy c u r r e n t s flowing i n s u c h a s p e c i m e n should a l s o show s i z e effects. F o r the c a s e of a t h i n p l a t e of t h i c k n e s s d we may u s e the d e c a y t i m e I" of eddy c u r r e n t s i n d u c e d by a m a g n e t i c f i e l d change p a r a l l e l to the s u r f a c e of the p l a t e to define a r e s i s t i v i t y PT" We find that this r e s i s t i v i t y has a f u n c t i o n a l d e p e n d e n c e upon lb/d which is d i f f e r e n t f r o m that c a l c u l a t e d by F u c h s 1) for the d i r e c t c u r r e n t r e s i s t i v i t y ~)F of s u c h a p l a t e . We may t h e r e f o r e u s e m e a s u r e m e n t s of PI" and ~F on a s i n g l e s p e c i m e n to o b t a i n both i t s e l e c t r o n i c m e a n f r e e path l b and its bulk r e s i s t i v i t y Pb. T h i s e l i m i n a t e s m o s t of the u n c e r t a i n t i e s p r e v i o u s l y p r e s e n t in d e t e r m i n a t i o n s of the i m p o r t a n t p r o p e r t y Pb" lb of m e t a l s f r o m s i z e effect i n v e s t i g a t i o n s r e q u i r i n g m e a s u r e m e n t s on s e v e r a l s p e c i m e n s of d i f f e r e n t t h i c k n e s s . T h e e l e c t r o m o t i v e f o r c e i n d u c e d in a coil s u r r o u n d i n g a p r i s m a t i c s p e c i m e n by d e c a y i n g eddy c u r r e n t s in the s p e c i m e n can be e x p r e s s e d as a s u m of e x p o n e n t i a l f u n c t i o n s of t i m e 2). F o r a thin 114

i n f i n i t e p l a t e of t h i c k n e s s d and r e s i s t i v i t y ~b the l o n g e s t t i m e c o n s t a n t of t h e s e e x p o n e n t i a l f u n c t i o n s is given by: to-

Uo d 2 2pb '

(1)

w h e r e ~o = 4~ × 10 -9 V s / A cm. T h i s d o m i n a n t t i m e c o n s t a n t can e a s i l y be m e a s u r e d by c o m p e n s a t i n g the i n d u c e d e . m . f with the voltage o v e r a s i m u l t a n e o u s l y d i s c h a r g e d c a p a c i t o r (fig. 1). O u r c a l c u l a t i o n shows that r e l a t i o n (1) also holds in the s i z e effect r e g i o n if ~) is r e p l a c e d by a p~- which is now a f u n c t i o n of lb/d. T h i s s i z e d e p e n d e n c e of 0v is c a u s e d by a p a r t i a l " i n e f f e c t i v e n e s s " of the e l e c t r o n s (analogous to that in the a n o m a l o u s s k i n effect 3)). T h e e l e c t r i c field is a n t i s y m m e t r i c a l about the c e n t r a l p l a n e of the p l a t e , and p a i r s of e l e c t r o n s m o v i n g in o p p o s i t e d i r e c t i o n s f r o m s u r f a c e to s u r f a c e without c o l l i s i o n s c o m p e n s a t e e a c h o t h e r . On the o t h e r hand, the f a c t that in the o r d i n a r y s i z e effect e v e r y e l e c t r o n c o n t r i b u t e s to the c u r r e n t l e a d s to q u i t e d i f f e r e n t s i z e d e p e n d e n c e s f o r the two r e s i s t i v i t i e s oI- and oF . S t a r t i n g f r o m the u s u a l a s s u m p t i o n s ( i . e . ,